The Senate Democratic leader says Sunday he's not trying to stop the testing or impede research, but he wants to make sure privacy policies are clear, transparent and fair to consumers.

“Here’s what many consumers don’t realize, that their sensitive information can end up in the hands of unknown third party companies,” he said at a press conference late Sunday morning. “There are no prohibitions and many companies say that they can still sell your information to other companies."

Various companies offer test kits as ways to learn more about one's health, heritage or family.

Many say they have strict rules about sharing any personal information and don't provide genetic data without scrubbing identities, getting users' consent or receiving a court order.

One company, MyHeritage, said Sunday it has never sold or licensed DNA data to any third party without the user's explicit, informed consent and never provides users' personal information to any third party.

In a statement reported by NBC News, a spokesman for Ancestry said, "We respect and agree with Sen. Schumer’s concern for customer privacy and believe any regulation should match the commitments we make to our customers."